In this section, we present extensive simulation results to validate the effectiveness of the proposed CTAD algorithm in 6G wireless networks.
For the URA scheme, we consider the case that every active device embeds its ID in the payload, in addition to the \(B = 360\)  information bits [1]}. It is assumed that there are total of \(\bar{K}=4096\)  devices in the network, therefore, \(B_{\mathrm {ID}} = \log _{2}(K) = 12\)  bits are required to encode the device ID.
Hence, each device transmits a total of \(B_{\mathrm {tot}} = B_{\mathrm {ID}}+B = 372\)  bits.
At the BS, the active devices are identified based on the ID embedded in the decoded payload. The active device separation error is evaluated by the packet error rate (PER) metric defined as \(\mathrm {PER}=\frac{\bar{K}_a}{{K_a}}\) , where \(\bar{K_a}\)  is the number of incorrectly decoded messages. If multiple messages with
the same device ID are decoded, they are discarded and
counted as an error. We assume that the pilot sequences obey an independent and identically distributed (i.i.d.) Gaussian distribution with zero mean and unit variance. Every \(\epsilon _i^k\)  of the BS-device channel is drawn from the complex Gaussian distributed random variables with zero mean and unit variance. The distance \(d_{\mathrm {DR},k}\)  from the \(k\) th device to the RIS is randomly generated from 500 m to 1000 m and from the RIS to the BS is 100 m. Note that the models in (REF ) and (REF ) are 3D channel models. We draw the central azimuth and elevation AoD from the RIS (AoA to the RIS) of each cluster uniformly over \([-180^{\circ },180^{\circ }]\)  and \([-90^{\circ },90^{\circ }]\) , respectively; draw the central azimuth AoA at the BS of each cluster uniformly over \([-90^{\circ },90^{\circ }]\) . The angular spread of each subpath is set as \(15^{\circ }\) . The over-complete bases \(\nu \)  and \(\varsigma \)  in (REF ) are uniform sampling grids covering \([-1,1]\) . The channel estimation accuracy is evaluated in terms of normalized
mean square error (NMSE) given by
\(\mathrm {NMSE}=\frac{1}{T_r}\mathop \sum \limits _{i=1}^{T_r}\frac{\left\Vert {\mathbf {G}}^i-\hat{\mathbf {G}}^i\right\Vert _F^2}{\left\Vert {\mathbf {G}}^i\right\Vert _F^2}\) , where \(T_r\)  is the number of Monte Carlo runs and \(\hat{\mathbf {G}}^i\)  is the device-RIS channel estimated at the \(i\) -th run. The tree-based decoder [1]} is employed in the simulation, where the \(B\) -bit message of each device is divided into \(L\)  subblocks of size \(B_1,\cdots ,B_{L}\)  satisfying the following conditions: \(\sum _{l}B_l=B\) , \(B_1=R\) , and \(B_l<R\)  for all \(i=2, \cdots , L\) .
Herein, all subblocks \(i=2,\cdots ,L\)  are augmented to size \(R\)  by appending the parity bits which are set to \(p_{b}(0,168,270)\) . Unless stated otherwise, we set \(R=270\) , \(N_1^{\prime }/N_1=N_2^{\prime }/N_2=1.5\) , \(\tau _p=N\) , \(\delta =10^{-6}\) , \(d=2\) , \(\tau _1=80\) , and \(\tau _2=80\) .
